LOUISVILLE, Ky.—If Kentucky coach John Calipari has his way, and he often does, his players will better resemble thoroughbreds than Wildcats as 2012 NCAA Tournament progresses. For UK to flourish as a championship contender, the next step must be taken at a sprint.

He wants them to push for fastbreaks and try to continue the attack through what some call a “secondary break” or others call “early offense.” Calipari calls it “playing random.”

At times, what he’s seen instead of running is jogging, allowing defenses to settle in and guard the Cats.

South Region No. 1 seed Kentucky (33-2) faces a third-round game Saturday evening at the KFC Yum! Center against No. 8 seed Iowa State (23-10) that will be one of the featured games of the weekend.

Most of the attention on that game is focused on how UK will cope with the unique presence of Iowa State’s Royce White, a bullish 6-8 forward who mostly runs his team’s offense as a point guard. He presents an uncommon challenge for any opponent.

For Kentucky to survive that game and advance toward the Final Four, however, it must become even more proficient on offense than in the 35 games that have led to this point. UK is 20th among Division I teams in scoring at 77 points per game and fourth in offensive efficiency according to KenPom.com. But, much as eventual champion North Carolina had room to improve when it began the 2009 tournament, the Wildcats can be better.

Freshman point guard Marquis Teague said playing slow is “not how we like to play. We can play that way if we have to, but we prefer to get out in transition. We want to get easy baskets. I don’t really want to slow down.”

In order to slow down, however, one must first be moving with speed. In the second-round win Thursday over Western Kentucky, the Wildcats were credited with only eight fastbreak points, same as in Sunday’s SEC championship game loss to Vanderbilt.

With Kentucky’s athletic ability, with finishers as punishing as freshman Michael Kidd-Gilchrist and Anthony Davis and a near-50-percent 3-point shooter in Doron Lamb to flare out in transition, the Wildcats ought to double that total regularly, and triple it on occasion.

“They’re athletic. They’re long. They’re going to get some dunks tomorrow,” Iowa State coach Fred Hoiberg said. “It’s just the way they play. You just have to try to limit their runs.”

The other element of Kentucky’s offensive evolution that continues to move gradually is making the passes that throw the defense off balance. The “extra pass” is the one that catches the opposing team leaning in the opposite direction and can set up players such as Kidd-Gilchrist and Davis for drives to the rim, senior Darius Miller for pull-up jumpers and Lamb for open threes on the opposite wing.

Kentucky had only 14 assists on 30 baskets against Western. It is credited with assists on only 48.2 percent of its field goals. No other No. 1 seed is below 57 percent.

That begins with UK’s point guard, the freshman Teague, who averages 4.7 assists despite being surrounded by scoring options and playing 32 minutes per game. Teague lately has been better in that department, starting with his brilliant 10-assist night in Kentucky’s early February home win over Florida, and following that with a combined 20 in three games against Vanderbilt.

“He’s grown a lot. In high school, he was a scoring guard, and now he’s like Chris Paul to me,” Kidd-Gilchrist said. “He’s underrated, I think.”

It’s funny that Kidd-Gilchrist would choose Paul as a comparison, because one of the obstacles Teague has had to face is being compared to Derrick Rose, Tyreke Evans, John Wall and Brandon Knight—the first one-and-done point guards who filled the point guard position as Calipari split the past four seasons between Memphis and UK.

“He’s even smarter than he was before, just reading the defense,” Kidd-Gilchrist said. “He’s maturing a lot.”